Device and method for detection and quantification of immunological proteins, pathogenic and microbial agents and cells

ABSTRACT

The present invention provides a method and device for detecting and quantifying the concentration of magnetic-responsive micro-beads dispersed in a liquid sample. Also provided is a method and microfluidic immunoassay pScreen™ device for detecting and quantifying the concentration of an analyte in a sample medium by using antigen-specific antibody-coated magnetic-responsive micro-beads. The methods and devices of the present invention have broad applications for point-of-care diagnostics by allowing quantification of a large variety of analytes, such as proteins, protein fragments, antigens, antibodies, antibody fragments, peptides, RNA, RNA fragments, functionalized magnetic micro-beads specific to CD 4+ , CD 8+  cells, malaria-infected red blood cells, cancer cells, cancer biomarkers such as prostate specific antigen and other cancer biomarkers, viruses, bacteria, and other pathogenic agents, with the sensitivity, specificity and accuracy of bench-top laboratory-based assays.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation application of U.S. patentapplication Ser. No. 13/684,618, filed Nov. 26, 2012, which is acontinuation-in-part application of U.S. patent application Ser. No.13/590,859, filed Aug. 21, 2012, which claims priority to U.S.Provisional Patent Application No. 61/539,210, filed Sep. 26, 2011, allof which are incorporated by reference herein in their entirety.

FIELD OF THE INVENTION

The present invention relates to the field of immunoassay andmicrofluidic devices and, in particular, to a point-of-care diagnosticmethod and device for the detection and quantification ofmagnetic-responsive micro-beads conjugated with proteins, cells andmicrobial agents dispersed in a liquid sample.

BACKGROUND OF THE INVENTION

Current immunoassay technologies for the detection and quantification ofproteins rely on the specificity of the chemical interaction betweenantigens and antigen-specific antibodies. These tests may be classifiedinto two main groups: laboratory based-tests and point-of-care (POC)tests. Laboratory-based tests are sensitive and accurate, but require alaboratory setting and skilled technicians. POC tests are designed to beused in the field and require limited training, but they are far lesssensitive and accurate with most POC tests providing only binarypositive/negative or semi-quantitative results.

All current immunoassay technologies involve the formation of anantigen-antibody complex. The detection of the complex indicates thepresence of a targeted analyte in a sample. The antigen-antibody complexis detected by measuring the emission and/or reflection of light by thecomplex, when fluorescent-tagged antigen-specific antibodies areemployed, or in the case in which antibody-coated micro-beads are used,by measuring the emission and/or reflection of light, or the magneticmoment of the micro-beads forming the antigen-bead complex. In allcases, optical or magnetic detectors and electronic readers arerequired.

For example, the simplest, best known and widely used POC diagnosticassay is the lateral flow assay, also known as the immunochromatic test.In this test, the targeted analyte is bound to an analyte-specificantibody linked to latex or gold nanoparticles. The presence of theanalyte in the sample then is revealed by the formation of a visibleband, or line, which results from the agglutination or accumulation ofthe analyte-antibody-linked complex. The band typically is visiblemacroscopically to the naked eye. Devices to increase the assay'ssensitivity have been developed which can read color changes withmicroscopic sensitivity. Fluorescent or magnetic-labeled particles alsohave been used. In these cases, however, electronic readers to assesstest results are needed. Thus, although sensitivity of the assay mayincrease, the cost and complexity of the assay also increases.

In recent years, antibody-coated micro-beads have been increasingly usedfor the separation and detection of proteins. In the field ofimmunoassay diagnostics, the concentration of micro-beads is a proxy forthe concentration of targeted proteins in a sample. In theseapplications, it is necessary to identify the concentration ofmicro-beads in the sample solution. The micro-beads may be mademagnetically responsive by adding a magnetic core or layer to a polymerbead. The micro-beads then may be coated with a variety of molecules andproteins, referred to as ligands, which serve the purpose of binding thetargeted antigen via an antibody-antigen interaction. In addition,fluorescent dyes can be incorporated into the micro-beads making themoptically detectable. Recently, a diagnostic test for the proteintroponin using magnetic micro-beads has been proposed by Dittmer et al.(Philips Research Europe). In this assay, micro-beads coated withanti-troponin antibody are immobilized via antibody-troponin-antibodieson the surface of a micro-well with the aid of an applied magneticfield. The number of antibody-troponin-antibodies is measured byilluminating the bottom of the well and measuring the light reflected bythe immobilized micro-beads with an optical receiver. Methods for thedetection of E. coli also have been developed using immuno-magneticmicro-beads. In this case, the bacteria in the sample are measured bydetecting time-resolve fluorescence.

While micro-bead technology has matured in the last decade, thetechnology to quantify micro-bead concentration has lagged behind.Current methods include manual microscopes and automatic orsemi-automatic cell counters. Typically, micro-bead counting using amicroscope involves the manual, and often tedious, counting of beadsthrough a microscope objective. This method requires skilled techniciansin a laboratory setting, is time consuming and is subject to atechnician's interpretation. Cell counters require photo sensors todetect micro-beads automatically by measuring the light reflection of alaser beam hitting the micro-bead's surface. Cell counters, whileaccurate, are expensive and also require skilled technicians insophisticated laboratory settings. Lab-on-a-chip devices to detect andmeasure the concentration of protein-coated micro-bead concentrationalso have been developed. These devices, however, rely on traditionalapproaches, i.e., light reflection and detection using micro-scale lightand photo sensors and micro-scale magneto-resistance magnetometers.Thus, while greatly reducing the need for a laboratory setting andequipment, lab-on-a-chip devices still require electrical readers andtransducers. In addition, these devices typically include handset andconsumable components, resulting in increased manufacturing, calibrationand maintenance costs. Thus, these devices have limited applications inthe field of POC immunoassay diagnostics.

There exists a need, therefore, for a POC immunoassay device which hasthe sensitivity and specificity of laboratory-based immunoassay testswhile being simple to use and low cost, as well as for methods to detectand quantify magnetic-responsive micro-bead concentration in a samplespecimen.

SUMMARY OF THE INVENTION

The pScreen™ microfluidic immunoassay device, based on the inventionsdisclosed herein, fulfills all of the above-described needs in a singledevice. The detection and quantification of an unknown concentration ofanalyte in a liquid sample is obtained by exploiting the fluid-dynamicproperties of magnetic-responsive micro-beads in liquid solution ratherthan using optical effects or magnetic field sensing as in currenttechnologies. The unknown concentration of the target analyte is derivedby measuring the differential flow rate between the sample flow in twomicro-channels, one of which is under the influence of an appliedmagnetic field gradient. The present invention significantly reduces thecost and complexity of current laboratory-based immunoassay diagnostictests, and greatly increases one-thousand fold the sensitivity oflateral flow tests, while maintaining the specificity and accuracy oflaboratory-based tests, and the ability to detect targeted antigenconcentration over a predefined range.

In an embodiment of the present invention, there is provided a method ofdetecting and quantifying the concentration of magnetic-responsivemicro-beads in a fluid. The method comprises measuring flow rate (Qm) ofa fluid in at least one test micro-channel (Cm) exposed to a magneticfield gradient with flow rate (Qo) of the fluid in a calibrationmicro-channel (Co) not exposed to a magnetic field gradient, in whichthe micro-channels are kept at an equal and constant pressure,calculating the ratio Qm/Qo, the difference Qo−Qm, and the ratio(Qo−Qm)^(p)/(Qm)^(q), wherein p and q are derived through a calibrationprocess, wherein the ratios Qm/Qo and (Qo−Qm)^(p)/(Qm)^(q) are a proxyfor the number of magnetic-responsive micro-beads in the fluid, and thenquantifying the concentration of magnetic-responsive micro-beads in thefluid. The presence of magnetic-responsive micro-beads in the at leastone test micro-channel which is exposed to the magnetic field gradientcauses flocculation of the magnetic-responsive micro-beads in the fluidwhich reduces the flow rate of the fluid through the at least one testmicro-channel.

In another embodiment, there is provided a method for detecting andquantifying concentration of an analyte in a liquid sample. The methodcomprises adding a liquid sample to a liquid sample inlet of a reactionchamber. The reaction chamber has adsorbed on its surface a plurality ofimmobilized antigen-specific antibodies (Ab1) specific to an analyte.The surface of the reaction chamber also has a plurality ofmagnetic-responsive micro-beads desiccated thereon, in which each of theplurality of magnetic-responsive micro-beads is coated with anantigen-specific antibody (Ab2) specific to the analyte. The methodcomprises having the liquid sample incubate within the reaction chamber,which causes rehydration of the plurality of antibody-coatedmagnetic-responsive micro-beads as the liquid sample is added andagitated in the reaction chamber, which rehydration disperses theantibody-coated magnetic-responsive micro-beads in the liquid sample,binding the rehydrated antibody-coated magnetic-responsive micro-beadsas well as the antigen-specific antibodies immobilized on the surface ofthe reaction chamber to any analyte present in the liquid sample to formAb1-analyte-Ab2-coated magnetic-responsive micro-bead complexes on thesurface of the reaction chamber, having the liquid sample containing anyunbound antibody-coated magnetic-responsive micro-beads exit thereaction chamber through a chamber outlet and transfer through acontinuous fluid connection to a micro-channel splitter which bifurcatesto form a calibration micro-channel (Co) and at least one testmicro-channel (Cm). The at least one test micro-channel and thecalibration micro-channel are kept at an equal and constant pressure.The calibration micro-channel is in continuous fluid connection with agraduated column, and the at least one test micro-channel is incontinuous fluid connection with at least one graduated column. Each ofthe graduated columns has a graduated scale thereon. The methodcomprises measuring flow rate (Qm) of the liquid sample in the at leastone test micro-channel exposed to a magnetic field gradient with flowrate (Qo) of the fluid in the calibration micro-channel not exposed to amagnetic field gradient, in which the presence of any unboundantibody-coated magnetic-responsive micro-beads in the at least one testmicro-channel which is exposed to the magnetic field gradient causesflocculation of the antibody-coated magnetic-responsive micro-beads inthe liquid sample which reduces the flow rate of the liquid samplethrough the at least one test micro-channel, calculating the ratioQm/Qo, the difference Qo−Qm, and the ratio (Qo−Qm)^(p)/(Qm)^(q), whereinp and q are derived through a calibration process, wherein the ratiosQm/Qo and (Qo−Qm)^(p)/(Qm)^(q) are a proxy for the number ofmagnetic-responsive micro-beads in the liquid sample, which is a proxyfor the concentration of analyte in the liquid sample, and thenquantifying the concentration of analyte in the liquid sample.

In a further embodiment of the present invention, there is provided asingle use, portable, lab-on-card microfluidic pScreen™magnetic-responsive micro-bead concentration counter device fordetecting and quantifying the concentration of magnetic-responsivemicro-beads in a liquid sample. The microfluidic device is comprised ofa liquid sample inlet defined by an opening for accepting a liquidsample that contains a quantity of magnetic-responsive micro-beads. Theliquid sample inlet is in continuous fluid connection with a flowresistor, which is in continuous fluid connection with a micro-channelsplitter which bifurcates to form a calibration micro-channel (Co) andat least one test micro-channel (Cm). The calibration micro-channel andthe at least one test micro-channel are kept at an equal and constantpressure. The calibration micro-channel is in continuous fluidconnection with a graduated column, and the at least one testmicro-channel is in continuous fluid connection with at least onegraduated column. The at least one test micro-channel is exposed to amagnetic field gradient, which causes flocculation of themagnetic-responsive micro-beads in the at least one test micro-channel.The flocculation reduces the flow rate (Qm) of the liquid sample in theat least one test micro-channel compared to the flow rate (Qo) of theliquid sample in the calibration micro-channel. Each of the graduatedcolumns has a graduated scale thereon which provides a read-out of thetotal volume of the liquid sample collected in each of the graduatedcolumns, in which the total volume of the liquid sample collected in theat least one test micro-channel graduated column indicates theconcentration of magnetic-responsive micro-beads in the liquid sample.

In yet another embodiment of the invention, there is provided a singleuse, portable, lab-on-card microfluidic pScreen™ immunoassay device fordetecting and measuring an analyte in a liquid sample. The microfluidicimmunoassay device is an assembly of the microfluidic pScreen™ devicedescribed above and an immunoassay reaction chamber.

In particular, the microfluidic pScreen™ immunoassay device comprises aliquid sample inlet defined by an opening for accepting the liquidsample. The liquid sample inlet is in continuous fluid connection with aflow resistor channel, which is in continuous fluid connection with anassay inlet of a reaction chamber. The reaction chamber has adsorbed onits surface a plurality of immobilized antigen-specific antibodies (Ab1)specific to an analyte, as well as having a plurality ofmagnetic-responsive micro-beads desiccated thereon. Each of theplurality of magnetic-responsive micro-beads is coated with anantigen-specific antibody (Ab2) specific to the analyte. Flow of theliquid sample through the reaction chamber rehydrates the plurality ofantibody-coated magnetic-responsive micro-beads which disperses into theliquid sample. Any analyte present in the liquid sample binds to thedispersed antibody-coated magnetic-responsive micro-beads as well as tothe antigen-specific antibodies immobilized on the surface of thereaction chamber to form Ab1-analyte-Ab2-coated magnetic-responsivemicro-bead complexes. Any unbound antibody-coated magnetic-responsivemicro-beads exit the reaction chamber through an assay outlet, which isin continuous fluid connection with a micro-channel splitter thatbifurcates to form a calibration micro-channel (Co) and at least onetest micro-channel (Cm), which are kept at an equal and constantpressure. The calibration micro-channel is in continuous fluidconnection with a graduated column, and the at least one testmicro-channel in continuous fluid connection with at least one graduatedcolumn. The at least one test micro-channel is exposed to a magneticfield gradient, which causes flocculation of the magnetic-responsivemicro-beads in the at least one test micro-channel. The flocculationreduces the flow rate (Qm) of the liquid sample in the at least one testmicro-channel compared to the flow rate (Qo) of the liquid sample in thecalibration micro-channel. Each of the graduated columns has a graduatedscale thereon which provides a read-out of the total sample volumecollected in each of the graduated columns, in which the total samplevolume collected in the at least one test micro-channel graduated columnindicates the concentration of analyte in the liquid sample.

As described above, the ratios Qm/Qo and (Qo−Qm)^(p)/(Qm)^(q) are aproxy for the number of magnetic-responsive micro-beads in a liquidsample, which is a proxy for the concentration of analyte in the liquidsample.

The devices may be fabricated by methods which include, withoutlimitation, etching each of the micro-channels on a plastic substrateusing a laser etcher system and then sealing the top of each of themicro-channels in plastic by thermal bonding, and by injection moldcasting in plastic. Suitable plastic substrates, plastic sealing andinjection mold casting plastics include, without limitation,poly(ethylene terephthalate)glycol, poly(lactic-co-glycolic acid) andpoly(methyl methacrylate), respectively.

Liquid samples that can be assayed in accordance with the embodiments ofthe invention include, without limitation, water, plasma, serum, buffersolution, urine, whole blood, blood analogs, and liquid solutions fromdilution of solid biological matter or other biological fluids.

Analytes that can be detected and quantified in accordance with theembodiments of the invention include, without limitation, proteins,protein fragments, antigens, antibodies, antibody fragments, peptides,RNA, RNA fragments, functionalized magnetic micro-beads specific toCD⁴⁺, CD⁸⁺ cells, malaria-infected red blood cells, cancer cells, cancerbiomarkers such as prostate specific antigen and other cancerbiomarkers, viruses, bacteria such as E. coli or other pathogenicagents.

The magnetic field gradient in accordance with the invention isgenerated from two magnets aligned lengthwise with the at least one testmicro-channel and along opposite poles to expose the at least one testmicro-channel to the magnetic field gradient. The at least one testmicro-channel is located between a gap formed between the opposite polesof the magnets. In another embodiment, the magnetic field gradient isgenerated by one magnet and a magnetic-responsive structure positionednear the at least one test micro-channel.

In accordance with the invention, the magnetic field generated can rangebetween about 0.05 Tesla (T) to about 0.5 T, and the magnetic fieldgradient that is generated can be about 10 T/m or greater.

The total sample volume collected in the calibration micro-channelgraduated column serves as a control for parameters such as variation inviscosity between samples, level of hematocrit in blood samples,temperature and humidity fluctuations and sample volumes.

In one embodiment of the invention, the micro-channel splitter of themicrofluidic devices bifurcates to form one test micro-channel and onecalibration micro-channel.

In another embodiment of the invention, the micro-channel splitter ofthe microfluidic device bifurcates to form three test micro-channels andone calibration micro-channel, in which each of the three testmicro-channels is in continuous fluid connection with one graduatedcolumn.

In another embodiment of the invention, the micro-channel splitter ofthe microfluidic device bifurcates to form four test micro-channels andone calibration micro-channel, in which the four test micro-channelsmerge to be in continuous fluid connection with one graduated column.

The present invention will be more fully understood from the followingdescription of the invention and by reference to the figures and claimsappended hereto.

BRIEF DESCRIPTION OF THE DRAWINGS

A fuller understanding of the invention can be gained from the followingdescription when read in conjunction with the accompanying drawings inwhich:

FIG. 1 is a schematic illustration of the method for determining thenumber of magnetic-responsive micro-beads in a fluid, in which the ratiobetween the flow rate in the calibration micro-channel (Co) and the testmicro-channel (Cm) is measured, according to the embodiments of theinvention;

FIG. 2 is a schematic illustration of the microfluidic pScreen™magnetic-responsive micro-bead concentration counter device, having onetest micro-channel and one calibration micro-channel, according to theembodiments of the invention;

FIG. 3 is an artistic rendering of the microfluidic pScreen™ immunoassaydevice, according to the embodiments of the invention;

FIG. 4 is a schematic illustration of the microfluidic pScreen™magnetic-responsive micro-bead concentration counter device, havingthree test micro-channels and one calibration micro-channel, accordingto the embodiments of the invention;

FIG. 5 is a schematic illustration of the microfluidic pScreen™magnetic-responsive micro-bead concentration counter device, having fourtest micro-channels and one calibration micro-channel, according to theembodiments of the invention;

FIG. 6 is the schematic illustration of the method for determining theconcentration of analyte in a fluid, in which the sample analyte isbound to immobilized analyte-specific immobilized antibodies and toanalyte-specific coated magnetic-responsive micro-beads, the ratioQ_(m)/Q_(o), of the flow rate Q_(o) in the calibration micro-channel,Co, and the flow rate, Q_(m), in the test micro-channel, Cm, ismeasured, according to the embodiments of the invention.

FIG. 7 is a schematic illustration of the pScreen™ immunoassay device,according to the embodiments of the invention;

FIG. 8 is a schematic illustration of three different views of areaction chamber of the pScreen™ immunoassay device, in which (A) showsthe secondary antibody (Ab2)-coated magnetic-responsive micro-beads andprimary antibody (Ab1)-capturing antibodies on the surface of thereaction chamber; (B) shows the Ab1-antigen-Ab2-magnetic-responsivemicro-bead complexes immobilized on the surface of the chamber; and (C)shows unbound, i.e., free, Ab2-magnetic-responsive micro-beads reachingthe assay outlet of the reaction chamber, according to the embodimentsof the invention;

FIG. 9 is a schematic illustration which shows the formation of theAb1-antigen-Ab2-magnetic-responsive micro-bead complexes as the samplewith the antigen flows through the reaction chamber and rehydrates themagnetic-responsive micro-beads, according to the embodiments of theinvention;

FIG. 10 is an artistic rendering of the pScreen™ immunoassay device,according to the embodiments of the invention;

FIG. 11 is a graph showing reduction in fluid flow rate, i.e., the ratiobetween flow rate in the test (with magnetic field) and calibration(without magnetic field) micro-channels versus the number ofmagnetic-responsive micro-beads in the flocculation region;

FIG. 12 is a photomicrograph showing magnetically-induced flocculationof magnetic-responsive micro-beads at a concentration of about 2,000micro-beads/μl in a test micro-channel, according to the embodiments ofthe invention; the inset shows the variation in flocculation at 300seconds, 600 seconds and 800 seconds;

FIG. 13 is a graph showing the concentration of magnetic-responsivemicro-beads in a solution obtained using the pScreen™ device versus thenominal concentration as tested by standard hemocytometry;

FIG. 14 is a graph showing the concentration of immunoglobulin (IgG) ina solution obtained using the pScreen™ immunoassay; and

FIG. 15 is a graph showing a calibration curve describing therelationship between (Vo−Vm)/(Vm)² and the concentration ofmagnetic-responsive micro-beads, according to the embodiments of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, the terms “magnetic-responsive micro-beads,” “magneticmicro-beads” and “micro-beads” are meant to be interchangeable.

As used herein, the terms “analyte” and “antigen” are meant to beinterchangeable.

As used herein, the terms “calibration micro-channel(s)” and “controlmicro-channel(s)” are meant to be interchangeable.

The present invention provides a flow rate-based method for detectingand quantifying the concentration, i.e., number, of magnetic-responsivemicro-beads in a fluid. The ratio, Qm/Qo, between the flow rate (Qm) ina test micro-channel (Cm) exposed to a localized high-gradient magneticfield, and the unperturbed flow rate (Qo) in a calibration, or control,micro-channel (Co) not exposed to the localized high-gradient magneticfield, is a monotonic function of the number of magnetic-responsivemicro-beads flowing through the test micro-channel. That is:Qm(N _(m))/Qo=ƒ(N _(m))  Equation (1)where Nm is the total number of magnetic-responsive micro-beadstransported by the fluid into the localized high-magnetic field region.Both micro-channels are held at an equal and constant pressure. As shownin FIG. 1, a fluid 12 seeded with magnetic-responsive micro-beads 15flows into two micro-channel inlets 14, 14′ and out of two micro-channeloutlets 16, 16′. The test micro-channel 22 on the right is exposed to ahigh-gradient magnetic field generated by two magnets 24, 24′. Themagnets are positioned as shown in FIG. 1 and in the inset. In anembodiment, the magnetic field gradient is generated by one magnet and amagnetic-responsive structure (not shown) positioned near the testmicro-channel 22. A magnetic-responsive structure may be made of ametallic material with ferromagnetic, super-paramagnetic or paramagneticproperties, such that upon application of an external magnetic field themagnetic-responsive structure generates an induced magnetic field. Thestructure is geometrically shaped, e.g., cylindrically-shaped, in orderto generate a magnetic field gradient in the region occupied by the testmicro-channel. Equation 1 applies to a wide range of magnetic-responsivemicro-bead concentrations, ranging from about 50 micro-beads/μl to about2×10⁶ micro-beads/μl. The upper and lower limits, however, are afunction of the micro-channels' size and magnetic field topology. Hence,both upper and lower limits may vary based on these parameters.

Because ƒ(Nm) is a monotonic function of Nm, it also holds that:N _(m)=ƒ⁻¹(Qm(N _(m))/Qo).  Equation (2)

Thus, according to Equation 2, the number of magnetic-responsivemicro-beads in a given fluid is a monotonic function of the ratio Qm/Qo.Thus, the number of magnetic-responsive micro-beads can be determined bymeasuring the ratio Qm/Qo in the two micro-channels, configured as shownin FIG. 1. In other words, the ratio Qm/Qo is a specific proxy for thenumber of magnetic-responsive micro-beads in a given fluid.

The analytical form of the function depends on the geometry, i.e.,length and inner diameter of the two micro-channels, magnetic fieldtopology, and the size of the magnetic-responsive micro-beads. Inaddition, the difference Q_(o)−Q_(m), and the ratio(Q_(o)−Q_(m))^(p)/(Q_(m))^(q), where p and q are derived through acalibration process, are a proxy for the number of magnetic-responsivemicro-beads in the fluid. The parameters p and q are obtained asfollowed. A solution containing a known concentration of micro-beads andof known volume is passed through the micro-channels and the flow rateQm and Qo are measured. Then, a solution containing the sameconcentration of magnetic-responsive micro-beads but of larger volumesimilarly is passed through the micro-channels. This process is repeatedseveral times. Then, the ratio (Qo−Qm)^(p)/(Qm)^(q), with p and q setequal to 1, are plotted versus the volume of each sample. Using thewell-known least square regression method, p and q are determined byenforcing the condition that the ratios (Qo−Qm)^(p)/(Qm)^(q) versussample volume form a horizontal straight line with slope equal to zero.

The present invention further provides a microfluidic pScreen™magnetic-responsive micro-bead concentration counter device fordetecting and quantifying magnetic-responsive micro-bead concentrationin a liquid sample. This device leverages the previously described flowrate-based detection and quantification method.

FIGS. 2 and 3 show the pScreen™ microfluidic device 5 for the detectionand quantification of magnetic-responsive magnetic beads in a liquidsample of the present invention. The microfluidic device 5 comprises aliquid sample inlet 8 in which a liquid sample, or specimen, whichcontains an unknown amount of magnetic-responsive micro-beads, isapplied. From the liquid sample inlet 8, the liquid sample,self-propelled by capillary action, flows through a flow resistor 32(shown in FIG. 3) and enters a micro-channel splitter 18. Themicro-channel splitter 18 bifurcates into two smaller micro-channels: acalibration micro-channel 20 and a test micro-channel 22. The twomicro-channels 20, 22 are identical in length and inner diameter (bestshown in FIG. 2).

The concentration of magnetic-responsive micro-beads that can bedetected and quantified using the methods and devices of the inventionis about 50 micro-beads/μl to about 2×10⁶ micro-beads/μl; and thediameter of the magnetic-responsive micro-beads is about 0.2 μm to about20 μm. In an embodiment, the diameter of the magnetic micro-beads isabout 4.0 μm.

In accordance with the invention, the test micro-channel and thecalibration micro-channel are made of a capillary tube, in which thelength of the capillary tube is about 0.2 cm to about 20 cm. In anembodiment, the length of the capillary tube is about 3.0 cm to about7.5 cm. In another embodiment, the length of the capillary tube is about1.5 cm.

In an embodiment, the length of the calibration micro-channel 20 and thetest micro-channel 22 is about 0.2 cm to about 20 cm. In anotherembodiment, the length of the two micro-channels 20, 22 is about 3.0 cmto about 7.5 cm. In still another embodiment, the length of the twomicro-channels 20, 22 is about 1.5 cm.

In an embodiment, the inner diameter of the calibration micro-channel 20and the test micro-channel 22 is about 50 μm to about 500 μm. In anotherembodiment, the inner diameter of the two micro-channels 20, 22 is about50 μm.

A magnetic field gradient is applied only to the test micro-channel 22.The magnetic field gradient is generated by small rare-earth (e.g.,neodymium) permanent magnet and ferromagnetic (e.g., nickel, iron) polestructures (not shown) which serve as a magnetic concentrator 54 (shownin FIG. 3) specifically designed to concentrate the magnetic field,hence creating a high magnetic field gradient (of about 100 T/m). In thecalibration channel 20, the liquid sample flows freely at a very lowvelocity (Reynolds number around 1) and shear rate range (1 to 400 s⁻¹).In the test micro-channel 22, the magnetic field gradient inducesmicro-bead flocculation if magnetic-responsive micro-beads are presentin the sample. Even in very small concentrations, as low as <50micro-beads/μl, the flow rate through the test micro-channel 22 will bereduced due to the formation of the magnetically-induced micro-beadflocculation. After flowing through the calibration and testmicro-channels 20, 22, a volume of liquid sample is collected in twograduated columns 26, 26′, both of equal size and volume.

Each graduated column 26, 26′ has a graduated scale thereon 30 whichprovides an easy to interpret read-out system of the total sample volumecollected in each graduated column 26, 26′. The graduated columns' 26,26′ length and cross section, as well as the respective scales 30thereon, are designed to be visible to the naked eye. Unlike current POCread-out devices, the read-out system of the microfluidic device of thepresent invention does not require electrical transducers and/orsensors. As shown in FIGS. 2 and 3, both graduated columns 26, 26′ areclearly visible. As shown in FIG. 3, the microfluidic device 5 may beconfigured in a cartridge 58 which fits into a holder 56. The read-outobtained by the microfluidic device 5 can be determined at any time bydirect comparison of the fluid in the two graduated columns 26, 26′.

Referring now to FIG. 2, the micro-channel configuration provides forthe concentration of micro-beads to be a monotonic function only of thevolumes Vo and Vm (Vo and Vm are the volumes collected at themicro-channel outlets 16, 16′ of the calibration micro-channel 20 (Co)and test micro-channel 22 (Cm), respectively; shown in FIG. 1). Thisapproach allows the user to read out the result provided by the pScreen™microfluidic device of the present invention at any time while the assayis running or at any time after the assay has been completed.

Given the relationship in Equation (1), and because the flow rate in thecalibration micro-channel 20 is constant and the magnetic-responsivemicro-beads are uniformly distributed in the sample fluid, and bydefinition ρ=dN/dV and dV=Qdt, where N is the number of micro-beads, Qthe flow rate, and V the fluid volume, the below equations are satisfiedat any time instances:

$\begin{matrix}\begin{matrix}{t = {\int_{0}^{No}\frac{\mathbb{d}N^{\prime}}{\rho\; Q_{0}}}} \\{{= \frac{N_{0}}{\rho\; Q_{0}}},}\end{matrix} & {{Equation}\mspace{14mu}(3)} \\{t = {\int_{0}^{Nm}{\frac{\mathbb{d}N^{\prime}}{\rho\; Q_{m}}.}}} & {{Equation}\mspace{14mu}(4)}\end{matrix}$where, t is the time, ρ is the magnetic-responsive micro-beadconcentration in the sample specimen 12, Qo and Qm are the flow rates inthe calibration and test micro-channels 20, 22, respectively, No and Nmis the number of magnetic-responsive micro-beads passing through thecalibration and test micro-channels 20, 22, respectively, and the primesymbol inside the integral, dN′, indicates, according to standardconvention, that the integral operation is computed on N variable

It thus follows that:

$\begin{matrix}{\left. {{\left. {{{N_{0} = {g\left( N_{m} \right)}},{{with}\text{:}}}{{g(N)} \equiv \int_{0}^{Nm}}} \right)\frac{\mathbb{d}N^{\prime}}{Q(N)}},{{and}\text{:}}} \right){Q = {{\frac{Q_{m}}{Q_{0}}.{Thus}}\text{:}}}} & {{Equation}\mspace{14mu}(5)} \\{{N_{m} = {{g^{- 1}\left( N_{0} \right)}.{Since}}},} & {{Equation}\mspace{14mu}(6)} \\{{{N_{0} = {\rho\; V_{0}}},{and}}{{N_{m} = {\rho\; V_{m}}},{{we}\mspace{20mu}{have}\mspace{14mu}{that}\text{:}}}{{\rho\; V_{m}} = {g^{- 1}\left( {\rho\; V_{0}} \right)}}} & {{Equation}\mspace{14mu}(7)} \\{{{Hence}\text{:}}{\rho = {{F\left( {V_{0},V_{m}} \right)}.}}} & {{Equation}\mspace{14mu}(8)}\end{matrix}$

Thus, the pScreen™ microfluidic device of the present invention providesa comparative read-out system in which the magnetic-responsivemicro-bead concentration, ρ, is a monotonic function of only Vm, thevolume flowing through the test micro-channel 22 where themagnetic-induced flocculation forms and Vo, the volume flowing throughthe calibration micro-channel 20 without the magnetic-inducedflocculation.

The comparative read-out system of the pScreen™ microfluidic device ofthe present invention greatly simplifies the detection andquantification of magnetic-responsive micro-bead concentration in aliquid sample. In addition, this comparative read-out system has thesignificant advantage of virtually eliminating common-mode error (withthe calibration graduated column 26 acting as a control), such asvariation in viscosity between samples, level of hematocrit in bloodsamples, temperature and humidity fluctuation of the test environment,and sample volume. The pScreen™ microfluidic device of the presentinvention thus provides a stand-alone device for the detection andquantification of magnetic-responsive micro-bead concentration in liquidsamples over a wide range of concentrations and micro-bead sizes.

FIG. 4 shows an alternate embodiment of the microfluidic device 5 of theinvention. In this embodiment, the test micro-channel (Cm) is split intothree test micro-channels 22, 22′ which 22″ run parallel to one other.The three test micro-channels 22, 22′ and 22″ are of the same length buthave a different inner diameter from one another. Each testmicro-channel 22, 22′, 22″ is connected to a separate graduated column26. In an embodiment, the first test micro-channel 22 has an innerdiameter of about 50 μm to about 500 μm, the second test micro-channel22′ has an inner diameter of about 100 μm to about 250 μm, and the thirdtest micro-channel 22″ has an inner diameter of about 250 μm to about 5mm. In another embodiment, the first test micro-channel 22 has an innerdiameter of about 50 μm, the second test micro-channel 22′ has an innerdiameter of about 100 μm, and the third test micro-channel 22″ has aninner diameter of about 250 μm. The inner diameter of the calibrationmicro-channel 20 is such that the area of the cross-section of thecalibration micro-channel 20 is identical to the sum of the areas of thecross-sections of the three test micro-channels 22, 22′, 22″.

For a given amount of magnetic-responsive micro-beads entering each ofthe three test micro-channels 22, 22′ 22″, the third, largest testmicro-channel 22″ experiences the lowest reduction in flow rate, thesecond, middle-sized test micro-channel 22′ experiences a reduction inflow rate greater than in the third, largest test micro-channel 22″, andthe first, smallest test micro-channel 22 experiences the greatestreduction in flow rate. In addition, the first, smallest testmicro-channel 22 will tend to clog before the second, middle-sized testmicro-channel 22′ and the third, largest test micro-channel 22″, and themiddle-sized test micro-channel 22′ will tend to clog before the largesttest micro-channel 22″. Hence, the device in accordance with thisembodiment allows measurement of a wide range of concentrations ofmagnetic-responsive micro-beads, in which the first, smallest testmicro-channel 22 allows for finely-tuned measurements ofmagnetic-responsive micro-beads at low concentrations and the third,largest test micro-channel 22″ allows for gross measurements ofmagnetic-responsive micro-beads at high concentrations.

FIG. 5 shows an additional alternate embodiment of the invention. Inthis embodiment, the test micro-channel 22 (Cm) is split into fourmicro-channels which run parallel to each other. The four testmicro-channels 22 have the same length and inner diameter. In anembodiment, each of the four test micro-channels has an inner diameterof about 12.5 μm to about 125 μm. In another embodiment, each of thefour test micro-channels has an inner diameter of about 12.5 μm. Theinner diameter of the calibration micro-channel 20 is such that the areaof the cross-section of the calibration micro-channel 20 is identical tothe sum of the areas of the cross-sections of the four testmicro-channels 22, 22′, 22″.

The four test micro-channels 22 rejoin to connect to one graduatedcolumn 26. If no magnetic-responsive micro-beads flow into the fourtest-micro-channels 22 and the one calibration micro-channel 20, thenthe flow rate of the fluid through the calibration micro-channel 20 isthe sum of the flow rates in each of the test micro-channels. Equations(1) through (8) also apply in this embodiment, however, because thereare four parallel test micro-channels compared to one testmicro-channel, a greater volume of fluid can flow through the device ina shorter amount of time, thus allowing a user to obtain a read out ofresults of the pScreen™ microfluidic device in a shorter period of time.

The present invention also provides a flow rate-based method fordetecting and quantifying concentration of an analyte in a liquidsample. The analyte can include, without limitation, proteins, proteinfragments, antigens, antibodies, antibody fragments, peptides, RNA, RNAfragments, cells, cancer cells, viruses, and other pathogenic agents.

The method according to this embodiment comprises adding a liquid sampleto a liquid sample inlet of a reaction chamber. The reaction chamber hasadsorbed on its surface a plurality of immobilized antigen-specificantibodies (Ab1) specific to an analyte. The surface of the reactionchamber also has a plurality of magnetic-responsive micro-beadsdesiccated thereon, in which each of the plurality ofmagnetic-responsive micro-beads is coated with an antigen-specificantibody (Ab2) specific to the analyte. The method comprises having theliquid sample incubate inside the reaction chamber, which causesrehydration of the plurality of antibody-coated magnetic-responsivemicro-beads as the liquid sample is added and agitated in the reactionchamber, which rehydration disperses the antibody-coatedmagnetic-responsive micro-beads in the liquid sample, binding therehydrated antibody-coated magnetic-responsive micro-beads as well asthe antigen-specific antibodies immobilized on the surface of thereaction chamber to any analyte present in the liquid sample to formAb1-analyte-Ab2-coated magnetic micro-bead complexes on the surface ofthe reaction chamber, having the liquid sample containing any unboundantibody-coated magnetic-responsive micro-beads exit the reactionchamber through a chamber outlet and transfer through a continuous fluidconnection to a micro-channel splitter which bifurcates to form acalibration micro-channel (Co) and at least one test micro-channel (Cm).The at least one test micro-channel and the calibration micro-channelare kept at an equal and constant pressure. The calibrationmicro-channel is in continuous fluid connection with a graduated column,and the at least one test micro-channel is in continuous fluidconnection with at least one graduated column. Each of the graduatedcolumns has a graduated scale thereon. The method comprises measuringflow rate (Qm) of the liquid sample in the at least one testmicro-channel exposed to a magnetic field gradient with flow rate (Qo)of the fluid in the calibration micro-channel not exposed to a magneticfield gradient, in which the presence of any unbound antibody-coatedmagnetic-responsive micro-beads in the at least one test micro-channelwhich is exposed to the magnetic field gradient causes flocculation ofthe antibody-coated magnetic-responsive micro-beads in the liquid samplewhich reduces the flow rate of the liquid sample through the at leastone test micro-channel, and calculating the ratio Qm/Qo, the differenceQo−Qm, and the ratio (Qo−Qm)^(p)/(Qm)^(q), wherein p and q are derivedthrough a calibration process, and wherein the ratios Qm/Qo and(Qo−Qm)^(p)/(Qm)^(q) are a proxy for the number of magnetic-responsivemicro-beads in the liquid sample, which is a proxy for the concentrationof analyte in the liquid sample.

As shown in FIG. 6, a liquid sample 12 is added, Step 1, to a reactionchamber 34, which has adsorbed on its surface a plurality of immobilizedantigen-specific antibodies (Ab1) (not shown) and contains a pluralityof magnetic-responsive micro-beads coated with antigen-specificantibodies (Ab2) 15 desiccated on the surface of the reaction chamber34. In Step 1, by adding the liquid sample to the reaction chamber 34,the antibody-coated magnetic-responsive micro-beads 15 are rehydratedand the magnetic-responsive micro-beads 15, as well as theantigen-specific antibodies immobilized on the surface of the reactionchamber 34, bind to any analyte present in the liquid sample 12 to formAb1-analyte-Ab2-coated magnetic-responsive micro-bead complexes on thesurface of the reaction chamber 34, with any unbound magnetic-responsivemicro-beads 15 free to flow (Step 2) into two micro-channel inlets 14,14′ and out of two micro-channel outlets 16, 16′. The test micro-channel22 on the right is exposed to a high-gradient magnetic field generatedby two magnets 24. As described in the previous paragraph, the number ofmagnetic-responsive micro-beads in a liquid sample passing through twomicro-channels, a test micro-channel (Co) and a calibration, or controlmicro-channel (Cm), is proportional to the ratio, Q_(m)/Qo, between theflow rate (Qm) in a micro-channel (Cm) exposed to a localizedhigh-gradient magnetic field, and the unperturbed flow rate (Qo) in amicro-channel (Co) not exposed to the localized high-gradient magneticfield. Therefore, by measuring the flow rates Qm and Qo, theconcentration of analyte in the liquid sample can be determined. Themethod applies to a wide range of antigen concentration, from about 0.01ng/ml to about 1 μg/ml.

The present invention further provides a pScreen™ microfluidicimmunoassay device for the detection and quantification of proteins,protein fragments, antigens, antibodies, antibody fragments, RNA, RNAfragments, cells, cancer cells, viruses, and other pathogenic agents.This device leverages the previously described method for detecting andquantifying concentration of an analyte in a liquid sample.

Principle of Operation

In one embodiment of the invention, as shown in FIG. 7, the pScreen™microfluidic immunoassay device 10 has a liquid sample inlet 8, a flowresistor channel 32, a reaction chamber 34, a micro-channel splitter 18,a test micro-channel 22, a calibration micro-channel 20 and graduatedreadout columns 26, 26′. In use, a liquid sample, or specimen, which maycontain an unknown amount of a target analyte, is applied into theliquid sample inlet 8. By capillary action, the sample is self-propelledand transferred from the liquid sample inlet 8 into the reaction chamber34 via the flow resistor channel 32. The flow rate of the liquid sampleis determined by the cross-section and length of the flow resistorchannel 32 and the surface tension of the device material and sampleliquid, as well as by the binding kinetic reaction between the analyte,i.e., antigen, and antibody in the reaction chamber 34.

As shown in FIG. 8A, the reaction chamber 34 is coated withantigen-specific antibodies (Ab1) 46 immobilized onto the surface of thereaction chamber 34. The antigen-specific antibodies (Ab1) 46, referredto as capturing antibodies, may be primary or secondary antibodies. Theantigen-specific antibodies (Ab1) 46 are bound to the surface of thereaction chamber 34 via adsorption. The surface of the reaction chamber34 also is coated with magnetic-responsive micro-beads 50 bydesiccation. The magnetic-responsive micro-beads may be desiccated onthe same region of the device where Ab1 antibodies 46 are bound, or in aregion preceding where the Ab1 antibodies 46 are bound. Themagnetic-responsive micro-beads are coated with antigen-specificantibodies (Ab2) to form antigen-specific antibody-coatedmagnetic-responsive micro-beads 50. These antigen-specific antibodies(Ab2) may be primary or secondary antibodies. As the liquid sample flowsinto the reaction chamber 34 via an assay inlet 36, the antigen-specificantibody-coated magnetic-responsive micro-beads 50 are rehydrated anddispersed in the liquid, and any antigen molecules 48 contained in thesample bind to the antigen-specific antibodies (Ab1) 46 immobilized onthe surface of the reaction chamber, and to the antigen-specificantibodies (Ab2) coating the magnetic beads, formingAb1-antigen-Ab2-coated magnetic-responsive micro-bead complexes 52 (FIG.8B). The formation of Ab1-antigen-Ab2-coated magnetic-responsivemicro-bead complexes 52 anchors the bound antibody-coatedmagnetic-responsive micro-beads 50 onto the surface of the reactionchamber 34. After all antigen molecules 48 have reacted to form theAb1-antigen-Ab2-coated magnetic-responsive micro-bead complexes 52, anyunbound, i.e., free, antibody-coated magnetic-responsive micro-beads 50exit the reaction chamber via an assay outlet 38 (FIG. 8C), leavingbehind the bound antibody-coated magnetic-responsive micro-beads 50 inthe reaction chamber 34. FIG. 9 shows the formation of theAb1-antigen-Ab2-coated magnetic-responsive micro-bead complex 52 as aliquid sample containing an antigen 48 flows through the reactionchamber 34 and rehydrates the antibody-coated magnetic-responsivemicro-beads 50.

A negative liquid sample, i.e., a sample not containing detectabletraces of the targeted analyte, results in zero antibody-coatedmagnetic-responsive micro-beads anchored to the reaction chamber'ssurface, as the Ab1-antigen-Ab2-coated magnetic-responsive micro-beadcomplexes cannot form. An analyte (i.e., antigen)-positive sample, onthe other hand, results in antibody-coated magnetic-responsivemicro-beads anchored to the reaction chamber's surface via theAb1-antigen-Ab2-coated magnetic micro-bead complexes. Thus, the higherthe concentration of analyte in the liquid sample, the greater thenumber of magnetic-responsive micro-beads anchored to the reactionchamber's surface, and hence the fewer the number of freemagnetic-responsive micro-beads reaching the reaction chamber assayoutlet. In the extreme case of very high analyte concentration, allantibody-coated magnetic-responsive micro-beads will be anchored to thereaction chamber's surface, and none will exit through the reactionchamber's assay outlet.

After flowing through the reaction chamber, the liquid sample,self-propelled by capillary action, reaches the pScreen™ magnetic beadconcentration counter portion of the device (which principle ofoperation has been described previously). If the liquid sample flowinginto the test micro-channel and the calibration micro-channel containsno magnetic-responsive micro-beads, the flow rate in both the test andcalibration micro-channels will be identical, and thus the sample volumecollected in each of the graduated columns will be identical. The usereasily is able to observe that the volume of sample in each of thegraduated columns is of equal length. On the other hand, if the samplecoming from the micro-channel splitter contains magnetic-responsivemicro-beads in any concentration other than zero, the flow of the liquidin the test micro-channel will be retarded (due to themagnetically-induced flocculation of the magnetic micro-beads). Hence,the length of the volume of liquid in the test graduated column will beless than the length of the volume of liquid in the calibrationgraduated column by an amount proportional to the magnetic-responsivemicro-bead concentration in the volume of liquid flowing into thegraduated columns. In other words, the higher the magnetic-responsivemicro-bead concentration in the liquid reaching the test and calibrationmicro-channels, the greater the difference in the lengths of the volumeof liquid observed in the two graduated columns. The resultingdifference between the volumes of liquid collected in the two graduatedcolumns is easily visible to the naked eye.

In an embodiment of the pScreen™ microfluidic immunoassay device,described in detail above and shown in FIG. 4, the test micro-channel(Cm) is split into three test micro-channels 22, 22′ and 22″ which runparallel to each other. In another embodiment of the pScreen™microfluidic immunoassay device, described in detail above and shown inFIG. 5, the test micro-channel (Cm) is split into four micro-channels 22which run parallel to each other.

FIG. 10 shows the pScreen™ microfluidic immunoassay device 10, accordingto the embodiments of the invention, in which the calibration column isonly partially visible. In this embodiment, the read-out is taken whenthe portion of the calibration column that is visible changes color,i.e., fills up with liquid.

EXAMPLES

The present invention is more particularly described in the followingnon-limiting examples, which are intended to be illustrative only, asnumerous modifications and variations therein will be apparent to thoseskilled in the art.

Example 1 Scientific Basis and Technology Feasibility of the PresentInvention

(A) Introduction

The data presented herein describe the effect that flocculation ofmagnetic-responsive micro-beads in a micro-channel has on the flowresistance of liquid in the micro-channel. A liquid seeded withmagnetic-responsive micro-beads in a micro-channel that is exposed to amagnetic field gradient produces a localized micro-bead flocculation.This localized micro-bead flocculation results in a localized reductionof the cross section of the micro-channel, and thus in a localizedincrease of the flow resistance across the flocculation region. Theincrease in resistance, in turn, results in an increased pressure dropacross the flocculation region due to the energy loss in maintaining theflow across the reduced cross-section of the micro-channel. If theexternal forces responsible for the formation of the micro-beadflocculation are stronger than the flow shear-stress on the micro-beadsand their aggregates, the micro-beads' flocculation increases inmagnitude as more incoming micro-beads are added. In the case of aconstant-pressure driven flow (relevant to the present invention), theincreased pressure drop results in a reduction of the micro-channel flowrate. This study investigated and analyzed this phenomenon, and theresults are reported below. These experimental results provide thescientific basis upon which the pScreen™ technology and the presentinvention have been developed.

(B) Experimental Methodology

Experimental data with respect to the effect of magnetic micro-beadflocculation on flow rate in micro-channels are presented. FIG. 1 is anillustration of a constant pressure flow system comprised of twomicro-channels. Test micro-channel 22 (Cm) was exposed to ahigh-magnetic field gradient, while calibration micro-channel 20 (Co)served as a control. The pressure difference driving the flow betweenthe micro-channel inlets 14, 14′ and micro-channel outlets 16, 16′ wasequal between the two micro-channels 20, 22. A liquid sample seeded witha known concentration of magnetic-responsive micro-beads 12 was added toboth micro-channels 20, 22 and the flow rate in both micro-channels 20,22 was recorded over time. Flocculation of the micro-beads was createdby means of a localized high-gradient magnetic field generated by twomagnets 24, 24′.

Experiments were conducted using micro-channels fabricated from glasscapillary tubes having an inner diameter of 50 μm and 100 μm. The lengthof the capillary tubes was varied between 3.0 cm and 7.5 cm. Themagnetic field was generated by two neodymium-iron-boron (NdFeB)permanent magnets 24, 24′ (25 mm×6 mm×1.5 mm; maximum surface field: 0.3T). The magnets 24, 24′ were aligned length-wise along opposite poles.The test micro-channel 22 capillary tube exposed to the magnetic fieldwas placed between the gaps formed between the opposite poles of theNdFeB magnets 24, 24′.

Both micro-channel capillary tubes 20, 22 were partially inserted into arubber stopper portion of a glass vacutainer tube (not shown), leavingabout 0.5 cm of the ends of the capillary tubes visible. Each capillarytube inlet and outlet was inserted in a polystyrene tubing (not shown)having an inner diameter of 360 λm, which tightly fit the 360 μm outerdiameter of the two micro-channel capillary tubes 20, 22. One end of thetubing lead directly to a reservoir containing the liquid sample withthe magnetic micro-bead solution 12, and the other end of the tubinglead to the vacutainer tubes which collected the fluid exiting themicro-channel outlets 16, 16′. The sample reservoir 12 was open to theair, and thus was at atmosphere pressure. The vacutainer tubes weresealed and kept under a constant vacuum. The pressure difference betweenthe sample reservoir 12 and the vacutainer tubes induced the liquidsample to flow from the reservoir into the vacutainer tubes. Thepressure difference was maintained at 0.6 mmHg per cm of capillary tubeto provide equal flow rate across capillary tubes of different lengths.Experiments were run in tandem, using two capillary tubes: one for thecalibration, i.e., control, micro-channel 20; and one for the testmicro-channel 22 exposed to the magnetic field gradient. Bothmicro-channel capillary tubes 20, 22 were kept at the same differentialpressure and drew fluid from the same sample reservoir 12. In thecalibration micro-channel capillary tube 20, the sample flowed freely.In the test micro-channel capillary tube 22, the applied magnetic fieldgradient induced micro-bead flocculation. The calibration and testmicro-channels 20, 22 were run simultaneously to eliminate common error,such as variation in atmospheric pressure, changes in viscosity due tofluctuation in temperature, and variations in micro-bead concentration.The suspension medium was 35% (by wt.) glycerol and 65% water to achievea viscosity similar to that of blood (about 3.6 cP). Green fluorescentdye was added to the suspension medium to increase visibility of thesolution exiting the two micro-channel capillary tubes 20, 22. Alsoadded to the medium were smooth carboxyl magnetic micro-beads(Spherotech, Inc.) with a diameter of 4.7 μm or 8.3 μm. Tests wereconducted with a micro-bead concentration between 100 micro-beads/μl and50×10³ micro-beads/μl. Sample volumes were between 50 μl to 200 μl andinitial flow rates were 0.01 μl/sec. As the sample fluid exited themicro-channel capillary tubes 20, 22, it formed small drops beforefalling into the vacutainer. The measurement of flow rate was calculatedby dividing the drop volume with the time interval between drops. Thefalling drop rate was recorded with a DVD video camera. Post videoanalysis provided the flow rate vs. time. Additional experiments wereconducted without a vacutainer. The micro-channel outlets 16, 16′ wereconnected to long polystyrene tubing (not shown) which was placed near agraduated ruler. The flow rate was measured by recording the advancementof the fluid meniscus inside the tubing as a function of time. Flow ratevalues in the glass calibration micro-channel capillary tube 20 notexposed to the magnetic field gradient were compared with theoreticalHagan-Poiseuille flow Q=(πa⁴)ΔP/(8 μL) (wherein a is the tube radius, ΔPis the pressure difference across the micro-channel, μ is the fluidviscosity, and L is the tube length) for a fully developed laminar flowof a Newtonian fluid in a cylindrical tube. Additional experiments wereconducted using a micro-channel configuration as shown in FIG. 2 andfabricated in poly(lactic-co-glycolic acid) (PLGA) and Polyethyleneterephthalate by laser etching as above described.

(C) Macroscopic Experimental Results and Data Analysis

FIG. 11 shows the normalized flow rate, i.e., the ratio between the flowrate in the test micro-channel capillary tubes (exposed to the magneticfield gradient) and the calibration micro-channel capillary tubes (notexposed to the magnetic field gradient) versus the number ofmagnetic-responsive micro-beads in the flocculation region. The numberof magnetic-responsive micro-beads is given by the product of the flowrate times the magnetic-responsive micro-bead concentration in thesample. The data show that the normalized flow rate is a monotonicfunction of the number (over three orders of magnitude) ofmagnetic-responsive micro-beads in the flocculation region. The amountby which the flow rate is reduced due to the pressure drop caused by theflocculation depends on the overall capillary length and the size of theflocculation zone. Thus, different aspect ratios of magnetic fieldlength along the micro-channels versus the total length of themicro-channels also were investigated. FIG. 13 shows three data curvesfor different aspect ratios of magnetic field (concentrator) lengthversus the total length of the micro-channels [ratios range from 0.17(triangle) to 0.24 (diamond) to 0.4 (square)]. To the investigators'knowledge, these data are the first to provide direct measurements ofthe effect of magnetic-responsive micro-bead flocculation on fluid flowrate in micro-channels.

(D) Data Analysis

These experimental data demonstrate that over a wide range thenormalized flow rate, Qm/Qo, is a monotonic function of the number ofmagnetic-responsive micro-beads entering the capillary tubes. What ispresented herein is a phenomenological model based on the Poiseuilleequation that the investigators derived to corroborate these results.The model relates the flow rate to the reduction in micro-channelcross-section due to the formation of flocculation. The model predictsthe following relationship between flow rate and number ofmagnetic-responsive micro-beads:{circumflex over (Q)}=1/(1+αN)  Equation (9)where cc is a parameter defined below:

$\begin{matrix}{{\alpha = {\left\lbrack {\left( {a/R_{eff}} \right)^{4} - 1} \right\rbrack/{LB}}},} & {{Equation}\mspace{14mu}(10)} \\{B = {\frac{3}{4}\left( {1 - ɛ} \right){\left( {a^{2} - R_{eff}^{2}} \right)/{r^{3}.}}}} & {{Equation}\mspace{14mu}(11)}\end{matrix}$where {circumflex over (Q)} is the normalized flow rate, defined asQm/Qo, N is the number of micro-beads in the flocculation, a is thecapillary tube radius, R_(eff) is the lumen length of the capillary tubenot blocked by micro-bead flocculation, L is the capillary tube length,r the radius of the micro-beads, ε is the porosity of the micro-beadflocculation in the test micro-channel, and B is a constant that isintroduced to collected different terms under a single parameter foradding simplicity and clarity to the equation form. The model predictswith high accuracy (solid lines, FIG. 11) the curve shift with changesin capillary length over magnetic field region lengths. This modelprovided analytical guidance for designing the specifications of thedevice of the present invention.(E) Microscopic Experimental Results

In order to observe the mechanism of magnetically-induced flocculation,microscopic studies were performed using an inverted microscope(Olympus, IX70, 20× magnification). This phenomenon was visualized usinga solution seeded with RBC-sized magnetic-responsive micro-beads, havinga diameter of 4 λm or 8 λm, in capillary tubes having a diameter of 50μm or 100 μm. FIG. 12 shows an example of flocculation formed in a 2,000micro-beads/μl analog solution. Flocculation initially formed at theleading edge of the magnet (corresponding to the greatest magnetic fieldgradient.) The size of the flocculation grew over the entire length ofthe magnetic field region. When the size of the flocculation covered thelength of the magnetic field region, the flocculation behaved as afluidized bed. Magnetic-responsive micro-beads downstream were released,while upstream incoming magnetic-responsive micro-beads were added tothe flocculation.

Example 2 pScreen™ Prototype Fabrication and Testing

(A) Fabrication

Two sets of pScreen™ prototypes were fabricated: (1) a bench topprototype with multiple micro-channels for simultaneous testing ofvarious samples; and (2) a single-use, portable, lab-on-card device. ThepScreen™ bench-top prototype was described in the previous section. ThepScreen™ lab-on-card prototype was realized using standard microfluidicsfabrication techniques. In brief, the micro-channels were etched using alaser etcher system on a poly(ethylene terephthalate)glycol (Petg)substrate. The channels then were sealed using a matchingpoly(lactic-co-glycolic acid) (PLGA) top by thermal bonding using a hotpress. The magnetic field gradient was obtained by placing two smallmagnets in an N—S configuration underneath the test channel. ThepScreen™ lab-on-card prototype also was fabricated using injection castmolding in which the prototype was fabricated in poly(methylmethacrylate) (PMMA).

(B) Experimental Data for a Microfluidic Device for Detecting andQuantifying the Concentration of Magnetic Micro-Beads

Two pScreen™ prototypes were tested using a variety of fluids such as,without limitation, blood, blood-analogs, or PBS buffer solution withdifferent concentrations of surfactant. Tests were conducted usingmagnetic-responsive micro beads having a diameter of 4.1 μm or 8 μm.Sample concentrations between 100 micro-beads/μl and 200,000micro-beads/μl were used. The concentration of magnetic-responsivemicro-beads was determined by recording the level of the fluid on thecalibration and test graduated column scales. Each mark on the scalecorresponded to a given amount of fluid volume which flowed through themicro-channels. The relationship derived in Equation 8 was applied toconvert the recorded volumes in magnetic-responsive micro-beadconcentration. The analytic expression of the relationship between thevolumes Vo and Vm, specific for the tested prototypes, was derived bycomputing Equations (5) through (8), with {circumflex over (Q)} given inEquations (9) through (11). To be especially noted is the fact that allof the equations provided above do not include time as a variable.Hence, it is not necessary to monitor/read the device's result at anyspecific time. The device reading at any time provides the sameread-out. FIG. 13 is a graph showing magnetic-responsive micro-beadconcentration measured using the pScreen™ device (y-axis) of the presentinvention versus magnetic-responsive micro-bead concentration measuredwith a standard hemocytometer (x-axis).

(C) Experimental Data for a pScreen™ Immunoassay

Several pScreen™ immunoassay prototypes were tested using buffersolutions containing various concentrations of mouse-IgG antibodyprepared by titration from a known concentration IgG standard. Theconcentration of mouse-IgG antibody ranged from 0.5 ng/ml to 100 ng/ml.Tests were conducted using magnetic-responsive micro-beads coated withanti-mouse IgG antibody and coating the surface of a reaction chamberwith anti-mouse IgG antibody. Sample volume ranged from 30 μl to 60 μl.The IgG antibody concentration was determined by recording the level ofthe fluid on the calibration and test graduated column scales. Each markon the scale corresponded to a given amount of fluid volume which flowedthrough the micro-channels. FIG. 14 is a graph showing the differencebetween the volume collected in the control column (Vo) and the volumecollected in the test column (Vm) (y-axis) versus the knownconcentration of IgG antibody (x-axis).

Examples 3 to 6 provide guidance regarding the detection andquantification of magnetic-responsive micro-beads and amount of analytein a liquid sample. Also provided are examples showing how to obtain aset of calibration curves for any embodiment by means of the claimedproxies herein, i.e., between the ratio Qm/Qo, the difference Qo−Qm, andthe ratio (Qo−Qm)^(p)/(Qm)^(q), and the number of magnetic-responsivemicro-beads and the concentration of analyte in a fluid. The examplesprovided show how to derive Equation 8 for any specific embodiment andprovide working examples for a selected embodiment. Equation 8 is adirect result of the claimed proxy between the ratio Qm/Qo and thenumber of magnetic-responsive micro-beads. Equation 8 converts thevolume of liquid sample passing through the control micro-channel, Vo,and through the test micro-channel, Vm, into the magnetic-responsivemicro-bead concentration and the analyte concentration in a liquidsample.

Example 3 Proxy Relationships Between Flow Rate and Micro-BeadConcentration

The present invention provides a method of detecting and quantifying theconcentration of magnetic-responsive micro-beads in a liquid sample, bycalculating the ratio Qm/Qo, the difference Qo−Qm, and the ratio(Qo−Qm)^(p)/(Qm)^(q), wherein p and q are derived through a calibrationprocess, wherein the ratios Qm/Qo and (Qo−Qm)^(p)/(Qm)^(q) are a proxyfor the number of magnetic-responsive micro-beads in the liquid sample,and then quantifying the concentration of magnetic-responsivemicro-beads in the liquid sample.

Three methods are provided to show how to use these proxy relationshipsand how to derive in practice the number of magnetic-responsivemicro-beads in a liquid sample. The first method analytically derivesthese relationships from the physical dimensions of a specificembodiment. The second method provides a calibration process thatenables the calibration of any embodiment. The third method teaches howto use the volume of sample passing through the control micro-channel,Vo, and through the test micro-channel, Vm, to derive the concentrationof magnetic-responsive micro-beads.

Method 1. Relationship Between Normalized Flow Rate, Qm/Qo, and Numberof Micro-Beads

The relationship between the normalized flow rate, Qm/Qo, and the numberof micro-beads entering the capillary tubes (i.e., micro-channels) isanalytically derived for a specific embodiment having the followingdimensions and values:

Test micro-channel and calibration (control) micro-channel: each with acircular cross-section with a radius of 50 μm; and a length of 15 mm.

Micro-beads: radius of 2 μm

Porosity of the flocculation: 0.55

Pressure difference between the inlet and outlet of both micro-channels:maintained constant at about 1 mmHg per cm.

The flow rate in the control micro-channel, Qo, is described by theHagen-Poiseuille equation, and is equal to:Q _(o) =ΔP/R _(o), with: R _(o)=8 μL/(πa ⁴)  Equation (12)where ΔP is the pressure drop across both micro-channels; Ro is themicro-channel's flow resistance; μ is the liquid sample viscosity; a isthe micro-channel's radius, and L is the micro-channel's length.

The flow rate in the test micro-channel, Qm, is given by:Q _(m) =ΔP/R _(m), with: R _(m)=8μ(L−λ)/(πa ⁴)+μλ(πa ² k),  Equation(13)where λ is longitudinal section of the length of the test micro-channeloccupied by the micro-bead flocculation; L−λ is the remaining length ofthe micro-channel flocculation-free; and k is the Darcy's constant. Thefirst term in Equation 13 is the Hagen-Poiseuille equation for theflocculation-free section of the test micro-channel, and the second termis Darcy's law for the section of the test micro-channel occupied by themicro-bead flocculation. Darcy's law is known by those skilled in theart to accurately describe flow of fluid through packed beads and beadflocculation. In this example, the Reynolds' number is low (<2)(Reynolds' number depends on an embodiment's physical dimensions andflow rates, and is a well know parameter that describes the physicalproperties of fluid in a flow), and thus the Darcy's constant takes theknown form:k=r ²ε³/(15(1−δ)²),  Equation (14)where ε is the porosity of the micro-bead flocculation in the testmicro-channel, i.e., the fraction of volume of the test micro-channelnot occupied by the micro-beads; and r is the micro-bead's radius.

Taking the ratio of Equation 13 over Equation 12, one gets:

$\begin{matrix}{{Q_{m}/Q_{o}} = {R_{o}/R_{m}}} \\{= {\frac{8\mspace{14mu}{µL}}{\pi\; a^{4}}/\left\lbrack {{8\;{{\mu\left( {L - \lambda} \right)}/\left( {\pi\; a^{4}} \right)}} + {\mu\;{\lambda/\left( {\pi\; a^{2}k} \right)}}} \right\rbrack}}\end{matrix}$

By rearranging the terms in the above equation, one gets:Q _(m) /Q _(o)=1/[1+(λ/8L)·(a ² /k−1)].  Equation (15)

It is noted that Equation 15 does not contain liquid sample viscosity.

The longitudinal section of the length of the test micro-channeloccupied by the micro-bead flocculation, λ, increases with the number ofmicro-beads, N, that have entered the test micro-channel and formed theflocculation under the effect of the magnetic field. These quantities, λand N, thus are related by the following identity:

$\begin{matrix}{{\lambda = {N/\hat{B}}},{{{with}\text{:}\mspace{14mu}\hat{B}} \equiv {\frac{3}{4}{{a^{2}\left( {1 - ɛ} \right)}/r^{3}}}}} & {{Equation}\mspace{14mu}(16)}\end{matrix}$where {circumflex over (B)} is a constant that is introduced to collectdifferent terms under a single parameter for adding simplicity andclarity to the equation.

By putting Equation 16 into Equation 15, one gets:Q _(m) /Q _(o)=1/[1+(N/8L{circumflex over (B)})(a ² /k−1)]  Equation(17)or alternatively,Q _(m) /Q _(o)=1/[1+{circumflex over (α)}N], where: α=(⅛L{circumflexover (B)})(a ² /k−1)

Equation 17 provides the relationship that enables the measurement ofthe number of micro-beads by measuring the ratio Qm/Qo. Thus, in thisexample, Equation 17 becomes:Q _(m) /Q _(o)=1/[1+2.63×10⁻⁶ ·N],  Equation (18)

In this example, Equation 18 is used as follows:

Given a fluid sample of unknown micro-bead concentration, for which theconcentration needs to be determined, the operator first runs the samplethrough the micro-channels as described above and measures periodicallythe flow-rates, Qm and Qo. The measurements can be done at any timewhile the liquid sample is flowing into the micro-channels. Then, byputting the ratio, Qm/Qo, obtained from each measurement into Equation18, the operator gets the number of micro-beads that have entered thetest micro-channel, N, at the time the flow rate measurements have beentaken. To compute the micro-bead concentration, the operator divides thevalue of N by the total volume of fluid that passed through the testmicro-channel at the time flow rate measurements have been taken, whichalso is equal to the sum of the products of the test micro-channel flowrates by the length of the time interval between measurements. Theshorter the time interval between measurements, the more precise is theobtained value of the number of micro-beads and of the micro-beadconcentration. Table 1 provides the values obtained in this example:

TABLE 1 Time Qo Qm Qo/ Vm Concentration (second) μl/sec μl/sec Qm N (μl)(beads/μl)  54 0.01 0.0100 1.000 0.0E+00  8.5 0.0E+00  906 0.01 0.00940.940 4.0E+04 17.1 2.3E+03 1818 0.01 0.0093 0.934 4.4E+04 26.1 1.7E+032778 0.01 0.0089 0.888 7.9E+04 35.0 2.3E+03 3786 0.01 0.0085 0.8451.1E+05 43.8 2.6E+03 4830 0.01 0.0082 0.816 1.4E+05 52.6 2.7E+03 59100.01 0.0079 0.789 1.7E+05 61.4 2.7E+03 7026 0.01 0.0076 0.763 1.9E+0570.3 2.8E+03 8190 0.01 0.0073 0.732 2.3E+05 79.1 2.9E+03 9390 0.010.0071 0.710 2.6E+05 87.8 2.9E+03 10614  0.01 0.0070 0.696 2.7E+05 96.62.8E+03

Table 1 shows the time in seconds at which each measurement was taken;the experimental measurements of the flow rate, Qo, in μl/second in thecontrol micro-channel; and the flow rate, Qm, in μl/second in the testmicro-channel. (For the method to work, it is not important how the flowrates, Qo and Qm, are measured. For example, the flow rates can bemeasured by using commercially available flow meters placed in serieswith the micro-channels, or as described in detail above in Example 1.The ratio, Qm/Qo, then is computed and shown in the table's fourthcolumn, from which the number of micro-beads, N, is derived usingEquation 18 and shown in the table's fifth column. The volume, Vm, iscalculated by taking the sum of the products of the test micro-channelflow rates by the length of the time interval between measurements, andis shown in the table's sixth column (alternatively, the volume, Vm,also can be measured as an independent variable, as described above).Then, micro-bead concentration is derived by dividing the N column bythe Vm column, with the result shown in the table's seventh column. Itis noted that the concentration slightly varies between measurements,and thus to obtain a more precise value, the average of thesemeasurements may be taken. In this example, the micro-bead concentrationis equal to 2,570 micro-beads/μl of liquid sample.

Equation 18 provided herein was derived for this specific embodiment. Aperson skilled in the art, however, would understand that following thesame process, the relationship between the normalized flow rate and thenumber of micro-beads entering the test micro-channel can be derived forother embodiments by putting the appropriate value of the Darcy'sconstant in Equation 15. The Darcy's constant is well known by thoseskilled in the art to depend on the micro-channels' shape, geometry,physical dimensions, design, flow rates, as well as an embodiment'sReynolds number. By using the appropriate Darcy's constant, theinvention may be practiced for other embodiments having, for example,non-cylindrical micro-channels and/or non-spherical micro-beads, and/ornon-uniformly-sized micro-beads.

In addition, for other embodiments, in which micro-bead flocculationdoes not occupy the entire test micro-channel's cross-section, but onlyoccupies outer layers, the relationship between the normalized flowrate, Qm/Qo, and the number of micro-beads entering the capillary tubesis given in Equations 9 to 11.

Method 2. Calibration Process

Provided herein is the construction of a set of calibration curves whichprovide the relationship between the normalized flow rate, Qm/Qo, andthe number of micro-beads entering the test micro-channels. The methoddescribed herein allows one to avoid the need to use complex analyticalexpressions, which for some embodiments may be too complex to berepresented in a mathematical closed form such as Equation 18.

For a given embodiment, the calibration process involves running aliquid solution containing a known concentration (the calibrationsolution) of magnetic-responsive micro-beads through the control andtest micro-channels, as shown in FIGS. 1 and 4. The flow rates, Qm andQo, then are measured at different time intervals and recorded, and thetotal volume passing through the test micro-channel also is recorded, asdescribed above. The shorter the time interval between recordings, themore precise is the resulting calibration curve. For each value of flowrate recorded, the number of micro-beads that have entered the testmicro-channel and added to the flocculation is computed by taking theproduct between the volume, Vm, passing through the test micro-channeland the value of the known concentration of the micro-beads. Then, theratio, Qm/Qo, for each measurement is plotted versus the number ofmicro-beads computed, as previously described. The process may berepeated multiple times using calibration solutions with different knownvalues of micro-bead concentration; the more times this process isrepeated, the more precise are the calibration curves. An example ofthese plots is shown in FIG. 11 for the embodiment described in theExample 1. Using this calibration curve, micro-bead number in any testedfluid of unknown concentration can be determined from the observedratio, Qm/Qo, by reading the horizontal value (the micro-bead number) onthe calibration curve corresponding with the vertical value (theobserved ratio, Qm/Qo) observed during the measurement. Theconcentration of the calibration solutions are prepared to approximatethe expected range of concentration of the liquid samples to be tested.

The same process can be repeated to derive calibration curves thatrelate the ratio, (Qo−Qm)^(p)/(Qm)^(q), with micro-bead concentration ina liquid sample. In this case, the parameters, p and q, are obtained asfollowed. A solution containing a known concentration of micro-beads andof known volume is passed through the micro-channels and the flow rates,Qm and Qo, are measured. Then, an identical solution is passed throughthe micro-channels but with a higher flow rate, Qo. This process isrepeated at least three times, with flow rates, Qo, which cover therange of flow rates, Qo, for which the embodiment is expected to beused. Then, (Qo−Qm)^(p)/(Qm)^(q), with p and q set equal to 1, areplotted for each solution versus the number of micro-beads entering thetest micro-channel (determined as previously described) to obtain a setof calibration curves. Then, p and q are independently varied until eachcurve (Qo−Qm)^(p)/(Qm)^(q) collapses on each other to form a singlecurve. A method to optimize p and q is to solve the following set ofequations.[(Q _(o) −Q _(m))^(p) /Q _(m) ^(p)]_(n) ¹=[(Q _(o) −Q _(m))^(p) /Q _(m)^(p)]_(n) ²[(Q _(o) −Q _(m))^(p) /Q _(m) ^(p)]_(n) ¹=[(Q _(o) −Q _(m))^(p) /Q _(m)^(p)]_(n) ³where the superscript numbers 1, 2, and 3 refers to the calibrationcurve number, and the subscript N indicates that the values of Qo and Qmin the square brackets are taken when the number of micro-beads enteringthe test micro-channel is equal to N. The value of N can be chosenarbitrarily, and the process may be repeated for different N values toobtain a more accurate value of p and q across the entire range ofnumbers of micro-beads.

Method 3. Conversion from Volume to Micro-Bead Concentration—Equation 8Working Example

Provided herein are two processes which may be used for any embodimentin order to convert the volume of sample passing through the controlmicro-channel, Vo, and the test micro-channel, Vm, intomagnetic-responsive micro-bead concentration and concentration ofanalyte in a liquid sample. The first process analytically derives theserelationships from the physical dimensions of the embodiment. The secondprocess provides a calibration method that enables calibration of anyembodiment and shows the use of the embodiment in practice.

Process A

Provided is a working example showing how Equations 5 through 8 enableone to derive the concentration of micro-beads in a liquid from theratio Qo/Qm, using the same dimensions provided above in Method 1(spherical micro-beads with a radius of 2 μm, micro-channels having alength of 15 mm and a radius of 50 μm and Qo equal to 0.0 μl/second),and for which the ratio, Qm/Qo, versus the number of micro-beads isprovided by Equation 18. By putting Equation 18 into Equation 5, onegets:

$\begin{matrix}{{N_{0} = {\int_{0}^{Nm}\frac{\mathbb{d}N^{\prime}}{\left( {1/\left( {1 + {\left( {2.63 \times 10^{- 6}} \right) \cdot N^{\prime}}} \right)} \right)}}}\ } & {{Equation}\mspace{14mu}(19)}\end{matrix}$where No is the number of magnetic responsive micro-beads that arepassing through the control micro-channel, Nm is the number of magneticresponsive micro-beads that are passing through the test micro-channel,and the prime symbol inside the integral, N′, indicates, according tostandard convention, that the integral operation is computed on an Nvariable. Equation 19 is the specific example, for a specificembodiment, of generic Equation 6. By solving the integral, one gets:

$\begin{matrix}{N_{o} = {N_{m} + {\frac{2.63 \times 10^{- 6}}{2}\left( N_{m} \right)^{2}}}} & {{Equation}\mspace{14mu}(20)}\end{matrix}$

Since No is equal to the product of the magnetic responsive micro-beadconcentration, ρ, times the volume of sample passing through the controlmicro-channel, Vo; and since Nm is equal to the product of the magneticresponsive micro-bead concentration, ρ, times the volume of samplepassing through the test micro-channel, Vm, Equation 20 can be rewrittenas:

$\begin{matrix}{{{{V_{o}\rho} = {{V_{m}\rho} + {\frac{2.63 \times 10^{- 6}}{2}\left( {\rho\; V_{m}} \right)^{2}}}};}{{or}\text{:}}{{V_{o} - V_{m}} = {\frac{2.63 \times 10^{- 6}}{2}\left( V_{m} \right)^{2}\rho}}} & {{Equation}\mspace{14mu}(21)}\end{matrix}$Equation 21 can easily be rearranged as follows:

$\begin{matrix}{\rho = {\left( {V_{0} - V_{m}} \right)/\left( {\frac{2.63 \times 10^{- 6}}{2}V_{m}^{2}} \right)}} & {{Equation}\mspace{14mu}(22)}\end{matrix}$

Equation 22 provides a simple expression that can be used to derive theconcentration of micro-beads for any liquid sample with unknownconcentration of micro-beads from the measurements of the volumes, Voand Vm, in this working example. In other words, Equation 22 is aspecific example of generic Equation 8. For example, a liquid samplecontaining an unknown concentration of magnetic-responsive micro-beadsis run through the control and test micro-channels, as described above.To obtain the value of this unknown concentration, the volume of thefluid passing through the control micro-channel, Vo, and the volume offluid passing through the test micro-channel, Vm, are recorded, asdescribed above. Then these values, Vo and Vm, are put into Equation 22to derive the concentration of magnetic-responsive micro-beads.

Process B

Provided herein is an example showing how to construct calibrationcurves for the relationship between volumes, Vo and Vm, andconcentration of micro-beads. The process allows one to avoid the needto use complex analytical expressions, which for some embodiments may betoo complex to be represented in a simple closed form such as Equation22. For a given embodiment, a series of solutions of known volume andcontaining known concentrations of magnetic-responsive micro-beads arepassed through the control and test micro-channels, as described above.The concentrations of these test (calibration) solutions are chosen tospan the entire range of micro-bead concentrations in the samples to betested. The volumes, Vo and Vm, then are measured. For the lab-on-cardmicrofluidic pScreen™ magnetic-responsive micro-bead concentrationcounter embodiment, the volumes, Vm and Vo, can be measured by readingthe scale on the control column (Co) and the test column (Cm). Once Vmand Vo have been recorded for all solutions, the ratios, (Vo−Vm)/(Vm)²,are plotted as a function of micro-bead concentration. This plotprovides a calibration curve that enables the invention to be reduced topractice. Using this calibration curve, the micro-bead concentration ofan unknown fluid can be determined from the observed difference, ratio(Vo−Vm)/(Vm)², by reading the horizontal value (micro-beadconcentration) on the calibration curve corresponding with the y value(Vo−Vm)/(Vm)² observed during the test, as shown in FIG. 15. Forexample, as shown in FIG. 15, if the measurement of Vm and Vo for asolution with an unknown micro-bead concentration gives a ratio of(Vo−Vm)/(Vm)² equal to 0.02, then the micro-bead concentration would be7500 micro-beads/μl. The calibration curve shown in FIG. 15 was obtainedusing the embodiment shown in FIG. 2, in which the micro-channels' radiiis 46 μm, the length of the micro-channels is 15 mm, and the radius ofthe micro-beads is 2.35 μm.

Example 4 Proxy Relationships Between Flow Rate and Concentration ofAnalyte in a Liquid Sample

The present invention provides a method of detecting and quantifying theconcentration of magnetic-responsive micro-beads in a liquid sample, bycalculating the ratio Qm/Qo, the difference Qo−Qm, and the ratio(Qo−Qm)^(p)/(Qm)^(q), wherein the ratios Qm/Qo and (Qo−Qm)^(p)/(Qm)^(q)are a proxy for the number of magnetic-responsive micro-beads in theliquid sample, which is a proxy for the concentration of analyte in theliquid sample, and then quantifying the concentration of analyte in theliquid sample, as described below.

As described above, the concentration of magnetic-responsive micro-beadsexiting the reaction chamber and entering the two micro-channels isproportional to the concentration of the analyte in the liquid sample.As described herein, the concentrations of these micro-beads aredetectable and quantifiable by either using the ratio Qm/Qo or thevalues Vo and Vm. Thus, in order to derive the concentration of analytein a liquid sample, the relationship between the concentration ofanalyte and the concentration of micro-beads exiting the reactionchamber needs to be calibrated. Two methods are provided, as follows:

Method 1

The first method consists of running a sample with a known concentrationof analyte through the reaction chamber and then counting the number ofmicro-beads binding to the reaction chamber's surface, as shown in FIGS.8 and 9. The number of micro-beads exiting the reaction chamber is equalto the total number of micro-beads deposited in the reaction chamber (asdescribed above) minus the number of micro-beads binding to the reactionchamber's surface. The process is repeated multiple times using a seriesof calibration samples obtained from the initial sample by titration.Then the concentration of micro-beads exiting the reaction chamberobtained for each calibration test is plotted as a function of theanalyte concentration. In practice, the sample with unknownconcentration of analyte is processed as described above andschematically shown in FIGS. 1 and 7. The concentration of micro-beadsentering the micro-channels, i.e., the concentration of micro-beadsexiting the reaction chamber, is derived as described above. Then, usingthe calibration curve derived and described above, the concentration ofmicro-beads is converted into the concentration of analyte.

Method 2

The second method enables the user to derive the calibration curve forany embodiment without counting the number of micro-beads binding to thereaction chamber's surface. To calibrate for any embodiment, a series ofsolutions of known volume, containing known concentrations of targetanalyte, are run through the device as described above. Theconcentrations of these test (calibration) solutions are chosen to spanthe entire range of expected analyte concentrations of the sample to betested. The difference, Vo−Vm, between the control micro-channel volume,Vo, and the test micro-channel volume, Vm, is measured for each testedcalibration sample and plotted as a function of the calibration sample'sanalyte concentration. Using this plot (calibration curve), the targetanalyte in any tested fluid can be determined from the observeddifference in volume, Vo−Vm, by reading the horizontal value (analyteconcentration) on the calibration curve corresponding with the verticalvalue (the Vo−Vm difference) observed in the test.

Example 5 Working Example—Quantification of Concentration of Micro-Beadsin a Liquid Sample

Quantification of the concentration of micro-beads in a liquid sample isperformed by using the pScreen™ immunoassay shown in FIG. 2, and havingthe dimensions as described above in Method 3, Process A. To measure theconcentration of micro-beads, the user performs the following steps:

-   -   Step 1: Take 50 μl of sample solution and place it on the device        inlet.    -   Step 2: Wait for the sample to flow into the device columns,        typically less than 20 minutes.    -   Step 3: Read the values of the fluid volumes, Vo and Vm, filling        up each column using the scale on the side of the column    -   Step 4: Compute the ratio (Vo−Vm)/(Vm)².    -   Step 5: The concentration of micro-beads is equal to ratio        (Vo−Vm)/(Vm)² divided by 1.3×10⁻⁶.

Example 6 Working Example—Quantification of Analyte Concentration in aLiquid Sample

Quantification of the concentration of an analyte in a liquid sample isperformed by using the pScreen™ immunoassay shown in FIG. 3, and thecalibration curve shown in FIG. 15. To measure the concentration of theanalyte, the user performs the following steps:

-   -   Step 1: Take 50 μl of sample solution and place it on the device        inlet.    -   Step 2: Wait for the sample to flow into the device columns,        typically less than 20 minutes.    -   Step 3: Read the values of the fluid volumes, Vo and Vm, filling        up each column using the scale on the side of the column    -   Step 4: Compute the ratio (Vo−Vm)/(Vm)².    -   Step 5: Read, on the calibration plot, the analyte concentration        on the horizontal axis of the calibration curve corresponding to        the value of the (Vo−Vm)/(Vm)² ratio on the vertical axis.

It will be appreciated by those skilled in the art that changes could bemade to the embodiments described above without departing from the broadinventive concept thereof. It is understood, therefore, that thisinvention is not limited to the particular embodiments disclosed, but itis intended to cover modifications that are within the spirit and scopeof the invention, as defined by the appended claims.

What is claimed is:
 1. A microfluidic immunoassay device for detectingand measuring an analyte in a liquid sample, comprising a liquid sampleinlet defined by an opening for accepting the liquid sample, said liquidsample inlet in continuous fluid connection with a flow resistorchannel, said flow resistor channel in continuous fluid connection withan assay inlet of a reaction chamber, wherein the reaction chamber hasadsorbed on its surface a plurality of immobilized antigen-specificantibodies (Ab1) specific to an analyte, wherein the surface of thereaction chamber also has a plurality of magnetic-responsive micro-beadsdesiccated thereon, each of said plurality of magnetic-responsivemicro-beads coated with an antigen-specific antibody (Ab2) specific tothe analyte, wherein the plurality of antibody-coatedmagnetic-responsive micro-beads rehydrate, disperse and bind to anyanalyte present in the liquid sample when the liquid sample flowsthrough the reaction chamber, wherein any analyte present in the liquidsample also binds to the antigen-specific antibodies immobilized on thesurface of the reaction chamber to form Ab1-analyte-Ab2-coatedmagnetic-responsive micro-bead complexes, and wherein any unboundantibody-coated magnetic-responsive micro-beads exit the reactionchamber through an assay outlet, said assay outlet in continuous fluidconnection with a micro-channel splitter which bifurcates to form acalibration micro-channel (Co) and at least one test micro-channel (Cm),said at least one test micro-channel and said calibration micro-channelkept at an equal and constant pressure, said calibration micro-channelin continuous fluid connection with a calibration graduated column, andsaid at least one test micro-channel in continuous fluid connection withat least one test graduated column, wherein one or more magnets createsa magnetic field gradient, said at least one test micro-channel exposedto the magnetic field gradient which causes flocculation of themagnetic-responsive micro-beads in the at least one test micro-channelwhich reduces flow rate (Qm) of the liquid sample in the at least onetest micro-channel compared to the flow rate (Qo) of the liquid samplein the calibration micro-channel, wherein each of the graduated columnshas a graduated scale thereon which provides a read-out of the totalsample volume flowing through the test micro-channel, Vm, and the samplevolume flowing through the calibration micro-channel, Vo, and collectedin each of the graduated columns, which read-out is proportional to theconcentration, ρ, of Ab1-analyte-Ab2-coated magnetic-responsivemicro-bead complexes, which is a function of the concentration of theanalyte in the liquid sample.
 2. The microfluidic immunoassay device ofclaim 1, wherein the ratio Qm/Qo, the difference Qo−Qm, and the ratio(Qo−Qm)^(p)/(Qm)^(q) are calculated, said ratios a proxy for the numberof magnetic-responsive micro-beads in the liquid sample, which is aproxy for the concentration of analyte in the liquid sample.
 3. Themicrofluidic immunoassay device of claim 1, wherein the magnetic fieldgradient is generated by two magnets aligned lengthwise with the atleast one test micro-channel and along opposite poles to expose the atleast one test micro-channel to the magnetic field gradient, said atleast one test micro-channel located between a gap formed between theopposite poles of the magnets.
 4. The microfluidic immunoassay device ofclaim 1, wherein the magnetic field gradient is created by one magnetand a magnetic-responsive structure positioned near the at least onetest micro-channel.
 5. The microfluidic immunoassay device of claim 1,wherein the magnetic field generated is between about 0.05 Tesla (T) toabout 0.5 T, and wherein the magnetic field gradient generated is about10 T/m or greater.
 6. The microfluidic immunoassay device of claim 1,wherein the total sample volume collected in the calibrationmicro-channel graduated column serves as a control for parameters suchas variation in viscosity between samples, level of hematocrit in bloodsamples, temperature and humidity fluctuations and sample volumes. 7.The microfluidic immunoassay device of claim 1, wherein each of thegraduated columns has a length of about 20 mm to about 200 mm, a widthof about 0.2 mm to about 3.0 mm, and a depth of about 0.1 mm to about1.0 mm, wherein the respective graduated scales thereon each have alength and a cross-section that is visible to the naked eye, and whereinthe read-out, providing a measurement of the unbound magnetic-responsivemicro-beads and hence of the concentration of analyte present in theliquid sample, can be obtained at any time by direct comparison of thetotal sample volume visualized in the calibration graduated column withthe at least one test graduated column.
 8. The microfluidic immunoassaydevice of claim 1, wherein the liquid sample is selected from the groupconsisting of water, plasma, serum, buffer solution, urine, whole blood,blood analogs, liquid solutions from dilution of solid biologicalmatter, and other biological fluids.
 9. The microfluidic immunoassaydevice of claim 1, wherein the analyte is selected from the groupconsisting of proteins, protein fragments, antigens, antibodies,antibody fragments, peptides, RNA, RNA fragments, functionalizedmagnetic micro-beads specific to CD⁴⁺, CD⁸⁺ cells, malaria-infected redblood cells, cancer cells, cancer biomarkers such as prostate specificantigen and other cancer biomarkers, viruses, bacteria such as E. coli,and other pathogenic agents.
 10. The microfluidic immunoassay device ofclaim 1, wherein the device is a single use, portable, lab-on-carddevice.
 11. The microfluidic immunoassay device of claim 1, wherein thedevice is fabricated by methods selected from the group consisting ofetching each of the micro-channels on a poly(ethyleneterephthalate)glycol plastic substrate, using a laser etcher system andthen sealing the top of each of the micro-channels in apoly(lactic-co-glycolic acid) plastic by thermal bonding, and byinjection mold casting in a poly(methyl methacrylate) plastic.
 12. Themicrofluidic immunoassay device of claim 1, wherein the concentration ofmagnetic-responsive micro-beads which can be detected and quantified isabout 50 micro-beads/μl to about 2×10⁶ micro-beads/μl, and wherein thediameter of the magnetic-responsive micro-beads is about 0.2 μm to about20 μm.
 13. The microfluidic immunoassay device of claim 1, wherein theat least one test micro-channel and the calibration micro-channel aremade of a capillary tube having a length of about 0.2 cm to about 20 cm.14. The microfluidic immunoassay device of claim 13, wherein bifurcationof the micro-channel splitter forms one, three or four testmicro-channels, and one calibration micro-channel.
 15. The microfluidicimmunoassay device of claim 14, wherein bifurcation of the micro-channelsplitter forms one test micro-channel and one calibration micro-channel,and wherein the one test micro-channel and the one calibrationmicro-channel have the same inner diameter of about 50 μm to about 500μm.
 16. The microfluidic immunoassay device of claim 14, whereinbifurcation of the micro-channel splitter forms three testmicro-channels and one calibration micro-channel, wherein each of thethree test micro-channels is in continuous fluid connection with onegraduated column, wherein the three test micro-channels each have adifferent inner diameter, wherein the one calibration micro-channel hasan inner diameter such that the area of the cross-section of the onecalibration micro-channel is identical to the sum of the areas of thecross-sections of the three test micro-channels, and wherein the firsttest micro-channel has an inner diameter of about 50 μm to about 500 μm,the second test micro-channel has an inner diameter of about 100 μm toabout 250 μm, and the third test micro-channel has an inner diameter ofabout 250 μm to about 5 mm.
 17. The microfluidic immunoassay device ofclaim 14, wherein bifurcation of the micro-channel splitter forms fourtest micro-channels and one calibration micro-channel, wherein the fourtest micro-channels merge to be in continuous fluid connection with onegraduated column, wherein the four test micro-channels have the sameinner diameter of about 12.5 μm to about 125 μm, and wherein the onecalibration micro-channel has an inner diameter such that the areas ofthe cross-section of the one calibration micro-channel is identical tothe sum of the areas of the cross-sections of the four testmicro-channels.